Homework Help

Math
Algebra
please prove all of number 6...

Question: please prove all of number 6...

Question details

Please prove all of number 6
6. (a) Let R be a commutative ring with identity. Prove that R is a field if and only if the only ideals of R are (0 and R. (b) Give an example of a ring that has exactly three ideals. (c) Show that M2(R), the ring of 2 x 2 matrices with entries from the real numbers, has no nontrivial proper two-sided ideals but is not a division ring

6. (a) Let R be a commutative ring with identity. Prove that R is a field if and only if the only ideals of R are (0 and R. (b) Give an example of a ring that has exactly three ideals. (c) Show that M2(R), the ring of 2 x 2 matrices with entries from the real numbers, has no nontrivial proper two-sided ideals but is not a division ring

Solution by an expert tutor

Blurred Solution

This question has been solved

Subscribe to see this solution